In the design and synthesis of energy systems, mathematical tools such as optimization algorithms are often used. While using them, environmental indicators are increasingly used as optimization criteria to exploit the possible environmental benefits of these systems. The problem is that the high number of environmental indicators poses a problem for optimization algorithms in terms of convergence, computational time and visualization. In this paper, this problem is addressed through a many-objective search of solutions using a state-of-the-art evolutionary algorithm, NSGA-III. Furthermore, the performance of this algorithm is tested using different settings in the PCA-based objective reduction framework. The original 14 indicators are reduced to seven, four, three and two, which reveal important insights about the use of NSGA-III, objective reduction and a combination of the two. It was found that by using objective reduction, the performance of NSGA-III can be further improved in terms of the quality of solutions and computational time. However, beyond a certain point, further objective reduction leads to a trade-off between solution quality and computational time. For this case study, the best quality solutions were obtained in the PCA reduction procedure when the CUT value was maintained at 99.99% without additional reduction in the last step, using a correlation matrix. The algorithms were applied to a real-life sizing case study involving hydrogen production from polymer-electrolyte-membrane (PEM) water electrolysis, for which the demand is furnished by the electricity spot market, solar photovoltaics (PV) or wind turbine in Marseille, France. These results will be useful for future applications of many-objective optimization and objective reduction. They will also be practical for including environmental indicators in the many-objective search for solutions.